Math Person: Question about 1) "Random" and then about 2) Win Probability


I am just a regular person, not a math expert. I don’t understand something.

Each week for my Fantastic Friday Lottery I use a random number generator on Google.
Like, this week I was picking 8 numbers from 1-69.

How is it, that just now the generator gave me #63 three times and #52 twice?

And, every week, at least one number is picked more than once.

If it were truly random, wouldn’t it pick all different numbers, instead of the same ones, over and over?

Helen (judohelen)

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As I understand computer programs generate pseudorandom numbers rather than truly random ones. Pseudorandom numbers are generated by algorithms and are determined by an initial value called a seed. If you provide the same seed to a pseudorandom number generator, it will produce the same sequence of numbers.

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Not necessarily.

Think of tossing a coin.

There are only two options - heads or tails. If it lands on heads the first time, that does not guarantee that it will land on tails the next time.

Each time you throw (or roll), every possible number has an equal chance of being chosen. It’s not like a raffle, where once you draw a ticket, that ticket is removed from the bucket and can’t be picked again.


Thanks for your replies!

Is there such a thing as a different number generator, which chooses numbers but doesn’t repeat until each number has been used once?

I was just thinking about if there was a solution! I searched ‘raffle generator’ in google, and found this link (and many others) - you put in your list of names, and then how many winners you want.

This was the first I looked at, there might be others that will suit you better. This one, you’d have to type a list of numbers into it first.

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much neater solution!

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Thanks so much to you both for your help!

I never would have thought to look that up!


Second Question:

If I use the Non-Repeating Random Number Generator, is there a way to tell people what is their chance of winning the lottery once?

In other words, can I say, in this Lottery, the usual number of entrants is 70, and the weekly number of winners is 8, so you have a 99% probability of winning this Lottery once, if you sign up for x consecutive weeks?

Or, since the numbers are really random, is there a chance someone could sign up for 150 weeks and never win?

P.S. I do make one-two Lotteries a year ones “for those who have never won” to prevent that from happening. Still, I am wondering!


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This is definitely possible, but I’m no maths-talking-guy, so I couldn’t tell you likelihoods.

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You should be able to calculate the probability like this to win exactly once in a number of specified weeks, if the number entrants are always the same
but it is 5am and I just woke up, so there might be errors


Thanks for your help!

This is new to me!


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Surely the chance of winning is never more than about 11.5 %, in any given week, because the same 8 people could, in theory, win every time. Your chances doesn’t increase because you enter several weeks, beyond the fact that by entering more than once, you obviously have more chance of winning than someone who only enters once.


Actually, the formula by @Aeranthes can be simplified to:
Probability to loose in one lottery = (E - w)/E

So probability to win at least once in C lotteries = 1 - ((E - w)/E)^C
If we want this probability to be greater than p:
1 - ((E - w)/E)^C > p
we need the number of lotteries to be:
C > log(1 - p)/log((E - w)/E)

For the @judohelen 's case with E = 70 entrants, w = 8 winners, p = 0.99 (we want 99 percent probability of winning at least once) you can simply write it to google and it computes the value:

You need to join at least 38 lotteries.


Not a math answer, but you can use the postbot to pick multiple numbers.


@postbot roll 8d69

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:game_die: 52, 23, 3, 52, 37, 31, 55, 31

2 52s!! I didn’t expect that!


Oh definitely, math is wonderful, they can literally win in row for 150 weeks and no chance on contrary!!

The mostly “random” in maths is really unique, there can be two numbers in sequence even if there are 1-70 entries for two winners, and both can be 6 & 69!!!(cause there is no rule for uniform distribution of probability!)
But i guess-- computer randomiser sometimes makes assumptions that as one number 4 is drawn, so it’ll move forward and draw later rather than in sequence (just my logic)
By the way-- the unpredictability about Guessing and " choosing " is what makes probability more beautiful

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Out of curiosity, i held few Lotteries few months back was using postbot to draw winner and i got #1 in two lottery and also won as #1 on some lottery, it was a coincidence or really “random”, i can’t decide!